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Working with Probabilities Physics 115a (Slideshow 1) A. Albrecht These slides related to Griffiths section 1.3. Consider the following group of people in a room:. Histogram Form. Consider the following group of people in a room:. Total people = 14.

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Working with Probabilities

Physics 115a (Slideshow 1)

A. Albrecht

These slides related to Griffiths section 1.3

















Assuming no age constraint, what is the probability of finding each age?

Related to collapse of the waveunction (“changing the question”)

Total people = 14


Assuming Age<20, what is the probability of finding each age?

Related to collapse of the waveunction (“changing the question”)

Total people = 14






Combine Red and Blue rooms age?

Total people = 29


  • Lessons so far age?

  • A simple application of probabilities

  • Normalization

  • “Re-Normalization” to answer a different question

  • Adding two “systems”.

  • All of the above are straightforward applications of intuition.



Most probable answer = 25 age?

Median = 23

Average = 21


Most probable answer = 25 age?

Median = 23

Average = 21

Lesson: Lots of different types of questions (some quite similar) with different answers. Details depend on the full probability distribution.


Average (mean): age?

  • Standard QM notation

  • Called “expectation value”

  • NB in general (including the above) the “expectation value” need not even be possible outcome.



Careful: In general age?

In general, the average (or expectation value) of some function f(j) is





Continuous Variables age?

Why not measure age in weeks?





Another case where a measure of age in weeks might by useful:

The ages of students taking health in the 8th grade in a large school district (3000 students).


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